Channel fading is a ubiquitous and fundamental characteristic of wireless communication systems. Fading deteriorates the link reliability of the wireless channel, thereby reducing system capacity and/or degrading user service experience. Diversity is a well-known principle that effectively combats wireless channel fading. The methods of achieving diversity include utilizing space, angle, polarization, frequency, time, and multipath. Diversity can be achieved at the transmitter and/or the receiver.
Consider the forms of diversity that can be realized by using multiple antennas at the transmitter and/or receiver of a wireless communication system. These are grouped under the categories of transmit and receive diversity respectively.
FIG. 1 illustrates a simplified diagram of a receiver 100 in a prior art wireless system that is equipped with multiple antennas (receive antenna 1 102, receive antenna N 102′) and exploits receive diversity. In this receiver 100, the multiple antennas (102. 102′) receive multiple versions of the same information-bearing signal. Assume that the wireless channel associated with any receive antenna is substantially statistically independent of the channel experienced by the other antennas. Then, the probability of each of the receive antennas being simultaneously faded is significantly smaller than that of any receive antenna being faded. Hence, the combined signal is much less likely to be faded, thereby improving the link reliability. In practice, the receive diversity gain is realized as follows. The signals received from the multiple receive antennas (102, 102′) are first individually processed with separate receive chains, each of which typically includes an analog signaling processing block (104, 104′), an analog-to-digital conversion block (106, 106′), and a digital signal processing block (108, 108′), respectively. The processed signals (109, 109′) are then combined in a combiner block 110. Combiner bock 110 may, for example, use selective combining or maximum ratio combining methods. The combiner 110 outputs signal 112, which may be subjected to further signal processing.
Similarly, FIG. 2 illustrates a simplified diagram of a transmitter 200 in a prior art wireless system equipped with multiple antennas (transmit antenna 1 202, transmit antenna N 202′) that exploits transmit diversity. In the FIG. 2 transmitter 200 illustrated here, the same information-bearing signal, source signal 204, is first split and pre-processed by splitter pre-processor 206 to generate multiple transmit signals (208, 208′), which are correlated with each other. These multiple transmit signals (208, 208′) are then individually passed through separate transmit chains including digital signal processing blocks (210, 210′), digital-to-analog conversion blocks (212, 212′), analog signal processing blocks (214, 214′) and transmitted with multiple antennas (202, 202′), respectively.
Transmit diversity refers to the realization of diversity gain by sending multiple, correlated signals over a channel from the transmitter. Typically, transmit diversity techniques make use of multiple transmit antennas to transmit these correlated signals. Firstly, transmit diversity is not straightforward to realize, in general. Transmitting the same signal through multiple transmit antennas typically results in no diversity gain whatsoever.
One of the earliest transmit diversity techniques that was proposed is delay diversity, in which the transmitter sends multiple copies of the same information with different delays through different antennas. A more sophisticated version of this scheme which uses two transmit antennas was proposed by Alamouti described in S. M. Alamouti, “A simple transmitter diversity scheme for wireless communications,” IEEE Journal on Selected Areas in Communication, vol. 16, pp. 1451-1458, October 1998.
Let the signal that is to be communicated be denoted by S(t) where t is assumed to be a discrete time instant. In the Alamouti scheme, two consecutive symbols are blocked off and transmitted over two time instants using the two antennas. Let X1(t) and X2(t) represent the output signals from the two antennas respectively, which may be expressed as
      [                                                      X              1                        ⁡                          (              t              )                                                                          X              1                        ⁡                          (                              t                +                1                            )                                                                                      X              2                        ⁡                          (              t              )                                                                          X              2                        ⁡                          (                              t                +                1                            )                                            ]    =      [                                        S            ⁡                          (              t              )                                                            -                                          S                *                            ⁡                              (                                  t                  +                  1                                )                                                                                      S            ⁡                          (                              t                +                1                            )                                                                          S              *                        ⁡                          (              t              )                                            ]  
Suppose that the time-varying channel responses from the two transmit antennas, e.g., two base station transmit antennas, to the receiver, e.g., a mobile receiver, are denoted by h1(t) and h2(t) respectively. For simplicity of explanation we can assume a flat channel but the more general case where the channel is frequency dependent can also be handled. If the channel coefficients are assumed to remain constant over two symbols, which is a mild assumption, the composite signal received by the mobile receiver can be represented byY(t)=h1X1(t)+h2X2(t)+W(t)Y(t+1)=h1X1(t+1)+h2X2(t+1)+W(t+1)which may be rewritten in terms of the original signal S(t) as
      [                                        Y            ⁡                          (              t              )                                                                        Y            ⁡                          (                              t                +                1                            )                                            ]    ⁡      [                                                                      h                1                            ⁢                              S                ⁡                                  (                  t                  )                                                      +                                          h                2                            ⁢                              S                ⁡                                  (                                      t                    +                    1                                    )                                                      +                          W              ⁡                              (                t                )                                                                                                                    -                                  h                  1                                            ⁢                                                S                  *                                ⁡                                  (                                      t                    +                    1                                    )                                                      +                                          h                2                            ⁢                                                S                  *                                ⁡                                  (                  t                  )                                                      +                          W              ⁡                              (                                  t                  +                  1                                )                                                          ]  or alternatively,
                    [                                                            Y                ⁡                                  (                  t                  )                                                                                                        Y                ⁡                                  (                                      t                    +                    1                                    )                                                                    ]            ⁡              [                                                            h                1                                                                    h                2                                                                                        h                2                *                                                                    -                                  h                  1                  *                                                                    ]              ⁡          [                                                  S              ⁡                              (                t                )                                                                                        S              ⁡                              (                                  t                  +                  1                                )                                                        ]        +      [                                        W            ⁡                          (              t              )                                                                                      W              *                        ⁡                          (                              t                +                1                            )                                            ]  
If the channel responses from the two transmit antennas to the receiver are known, it is straightforward to invert the transmitter code construction and extract the transmitted signal by the following transformation:
                              [                                                                                          S                    ^                                    ⁡                                      (                    t                    )                                                                                                                                            S                    ^                                    ⁡                                      (                                          t                      +                      1                                        )                                                                                ]                =                              [                                                                                h                    1                    *                                                                                        h                    2                                                                                                                    -                                          h                      2                                                                                                            -                                          h                      1                                                                                            ]                    ⁡                      [                                                                                Y                    ⁡                                          (                      t                      )                                                                                                                                        Y                    ⁡                                          (                                              t                        +                        1                                            )                                                                                            ]                                                  =                                            (                                                                                                              h                      1                                                                            2                                +                                                                                                h                      2                                                                            2                                            )                        ⁡                          [                                                                                          S                      ⁡                                              (                        t                        )                                                                                                                                                        -                                              S                        ⁡                                                  (                                                      t                            +                            1                                                    )                                                                                                                                ]                                +          noise                    which results in second-order diversity over a fading channel. The Alamouti scheme is simple, but requires the receiver to track the gains from each of the two transmit antennas separately, which normally requires two sets of pilots to be used. This is especially challenging in the cellular uplink, e.g., where a mobile device transmits to a base station receiver. Furthermore, the requirement of known transmit diversity techniques to use multiple transmitter chains, each of which normally includes both digital and analog signal processing blocks can be cost prohibitive in many applications.
In view of the above discussion, there is a need for improved methods and apparatus of achieving transmit and/or receive diversity in wireless communications systems. Methods and apparatus that achieve diversity while reducing the amount of signaling dedicated to pilots over known methods would be beneficial. Methods and apparatus that achieve diversity without the need for multiple transmit chains would also be beneficial.